One sample program (with its output) and 18 subroutines are listed in this appendix.

Topics: DTIC Archive, Parlett,B N, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

A program to solve a real cubic equation efficiently and as accurately as the data deserve is not yet an entirely cut-and-dried affair. An iterative method is the best found so far. This method plus some other issues, like accuracy, scaling, preconditioning and testing, are discussed in these notes in enough detail to convey an impression of what Numerical Analysis is about. Keywords: QBC computer program, Newton's iterations.

Topics: DTIC Archive, Kahan, W, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS, *COMPUTER...

The Lanczos algorithm generates Ritz values in order to approximate eigenvalues. If some eigenvalues are clustered then a Ritz value may hover at a wrong value for a good number of steps. We study this phenomenon and focus on the point of discovery, the first step at which it is certain that there is a hidden eigenvalue in the vicinity of stabilized Ritz values. Both before and after this point the Ritz value behavior is routine - but for different eigenvalue configurations. The effective...

Topics: DTIC Archive, Parlett, Beresford N, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED...

A simple test is given for determining whether a given matrix is the eigenvector matrix of an (unknown) unreduced symmetric tridiagonal matrix. A list of known necessary conditons is also provided. A lower bound on the separation between eigenvalues of tridiagonals follows from our Theorem 3. (Author).

Topics: DTIC Archive, Parlett,B N, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

Topics: DTIC Archive, Suhl, Harry, CALIFORNIA UNIV SAN DIEGO LA JOLLA INST FOR PURE AND APPLIED PHYSICAL...

The two sided Lanczos algorithm is known to suffer from serious breakdowns. These occur when the associated moment matrix does not permit triangular factorization. We modify the algorithm slightly so that it corresponds to using a 2 X 2 'pivot' in triangular factorization whenever a 1 X 1 pivot would be dangerous. The incidence of breakdown is greatly reduced. The price paid is that the tridiagonal matrix produced by the algorithm now has bumps whenever a 2 X 2 pivot is used. (Author)

Topics: DTIC Archive, Parlett, B N, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

A branch of Complexity Theory called Information-Based Complexity Theory (IBCT), produces an abundance of impressive results about the quest for approximate solutions to mathematical problems. Why then do most numerical analysts turn a cold shoulder to IBCT? Close analysis of two papers representative of IBCT's best efforts reveals a mixture of nice new observations, misdirected examples and misleading theorems. Some elements in the framework of IBCT, erected to support a rigorous yet flexible...

Topics: DTIC Archive, Parlett, Beresford, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

In this paper we discuss some numerical aspects of a particular construction of balanced biorthogonal multifilters by means of the lifting scheme. This construction allows, by simply solving linear equations, to obtain multifilters which do not need prefiltering, and for which the discrete versions of polynomial preservation/annihilation properties, are respectively, satisfied by their low and high-pass branches. In particular, we conduct experiments on how a parameter which appears in our...

Topics: DTIC Archive, Bacchelli, Silvia, Cotronei, Mariantonia, Lozzaro, Damiana, PADOVA UNIV (ITALY) DEPT...

Calculating M/N := A/B + or - C/D in lowest terms, given the integers A, B, C and D, is a task in Elementary schools; and it is an easy exercise in Computer Programming too provided the given integers must be less than half as wide as the widest integers that can be handled conveniently by the computer's hardware or by its programming language. But that program because becomes much more complicated (and slower) if it is naively expected to perform correctly whenever all six of our integers A,...

Topics: DTIC Archive, Kahan, W, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS, *FLOATING...

We complete the discussion of the periodic fixed points of Backlund transformations for the Korteweg-de Vries equation. It will be shown that the systems of equations defined by the KdV periodic fixed points are equivalent to the periodic Kac-Van Moerbeke systems. As a consequence, for even order fixed points, the KdV systems are equivalent to the periodic Toda lattice. The periodic fixed points of the Backlund transformation for the Boussinesq equation are found to have a Hamiltonian...

Topics: DTIC Archive, Weiss, John E, CALIFORNIA UNIV SAN DIEGO LA JOLLA INST FOR PURE AND APPLIED PHYSICAL...

As for back as 1821, in the Cours d'Analyze of the Ecole Polytechnique, Augustin Cauchy published a proof of the following remarkable result. If any row, together with its matching column, is deleted from a real symmetric matrix, then the eigenvalues of the new matrix interlace the eigenvalues of the old one. In the presence of more information, much more can be said about the interlacing of eigenvalues and the relationship between the space and the corresponding eigenvectors. An example of...

Topics: DTIC Archive, Hill, Jr , R O, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

A block reflector is an orthogonal, symmetric matrix that reverses a subspace whose dimensions may be greater than one. We shall develop the properties of block reflectors and give some algorithms for computing a block reflector that introduces a block of zeros into a matrix. We consider the compact representation of block reflectors, some applications, and their use in parallel computers

Topics: DTIC Archive, Schreiber, Robert, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

The two-sided Lanczos algorithm is known to suffer instability in the form of serious breakdown. This occurs when the associate moment matrix does not permit a triangular factorization. This work uses the notion of a generalized pivot to inexpensively circumvent the breakdown in most cases, with the 2x2 pivot examined in detail. The case where the generalized pivot is of no avail is analyzed, introducing a surprising characterization for that form of serious breakdown. (Author)

Topics: DTIC Archive, Taylor,Derek R, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

The authors consider the nested dissection ordering of a k x k grid of nodes and the Cholesky factorization of the associated k squared x k squared symmetric matrix. When the factorization is computed on a hypercube machine with p processors then the communication cost (the total number of nonzero elements that need to be communicated among the processors) can be kept down to O (pk squared) when the processors are assigned appropriately. This result was proved in George, Liu and Ng (1987). We...

Topics: DTIC Archive, Gao, F, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS, *COST...

This thesis consists of two parts. First, a condition number for the exponential of a triangular matrix S is introduced. It measures how sensitive is e sub s to relatively small perturbations in the elements of S. Second, a new technique (matrix argument reduction) for computing periodic matrix functions is described and discussed in detail. By applying this technique to the computation of e sub s one can always reduce the problem to one in which the eigenvalues lie close to the real axis.

Topics: DTIC Archive, Ng,K C, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

We present a problem data set for stochastic programming, and associated real world applications. The problem descriptions were collected from the literature, with emphasis on variety of problem structure and application. Each problem has a short description, mathematical problem statement, and notational reconciliation to a standard problem format. In addition, most problems have one or more corresponding data files in SMPS1 format.

Topics: DTIC Archive, Ariyawansa, K A, WASHINGTON STATE UNIV PULLMAN DEPT OF PURE AND APPLIED MATHEMATICS,...

A geometric approach is proposed for selecting the knots used in a parametric convexity-preserving B-spline approximation scheme. The approach automatically gives the necessary information about the shape suggested by the data which may be exact or not.

Topics: DTIC Archive, Morandi, R., Scaramelli, D., Sestini, A., PADOVA UNIV (ITALY) DEPT OF PURE AND...

Consider the task of finding all the eigenvalues of a dense matrix. We show how Hadamard's procedure (1891) can be organized into Aitken's H-table (1925) and how the H-table may be transformed into Rutishauser's qd-array (1953) with the help of the Lanczos algorithm. We show how the qd algorithm can be interpreted as defining the LR algorithm (1958). Finally we show how the original qd algorithm may be transformed into the shifted differential qd algorithm dqds developed by Fernando and Parlett...

Topics: DTIC Archive, Parlett, Beresford N., CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED...

This study is in the area of matrix eigenvalue computations The Householder-QR algorithm has become the standard method for diagonalizing a symmetric matrix. First the matrix is reduced to tridiagonal form T by a technique introduced by A. Householder in 1958. Next the tridiagonal matrix T is diagonalized by successive applications of the QR transformation with shifts Moreover it is well known that the QR transformation is backward stable. That means that the computed transform is exactly...

Topics: DTIC Archive, Le, J, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

This grant supported research by two University of California Berkeley graduate students on innovative numerical methods for flows around complex boundaries such as occur in solidification from the melt. New two-dimensional magnetization-based methods for complex fluid flows were developed and analyzed. New adaptive finite difference methods for simulation of the fluid flow in Czochralski growth were implemented and tested.

Topics: DTIC Archive, Strain, John, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

What does it mean to compute an eigendecomposition of an uncertain matrix? Because of measurement errors and roundoff errors, one must typically compute the eigenvalues and eigenvectors not of a single matrix but rather of a ball of matrices whose radius depends on the uncertainty in the data. We approach this problem by asking how to partition the eigenvalues of the matrices in the ball into nonoverlapping groups which cannot themselves be further partitioned. More specifically, we define the...

Topics: DTIC Archive, Demmel,James Weldon, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED...

A quadratic eigenvalue problem with symmetric positive definite coefficient matrics may be reduced to linear form while retaining symmetry in the new coefficients but neither of them will be positive definite. Formally the symmetric Lanczos algorithm and subspace iteration may be used to computer some eigenpairs of the linear problem. The trouble is that the basis vectors are orthogonal with respect to an indefinite inner product so there is no assurance that will be linearly independent....

Topics: DTIC Archive, Chen, H C, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

There have been many attempts to design systems which use computers for the manipulation of symbolic mathematical data. Existing systems begin to provide a useful level of assistance to engineers, applied mathematicians, scientific programmers, and others who must perform large-scale or in other ways tedious symbolic, algebraic computation, accurately, as part of their work. However, systems which are currently available suffer from the fact that they are generally weakly-structured collections...

Topics: DTIC Archive, Fateman, Richard J, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

The author pursued research to provide improved subroutines for common arithmetic functions for scientific computations. He produced an algorithm for the accurate implementation of rational arithmetic operations without resorting to mult-precision arithmetic. This was described in a paper entitled Rational arithmetic in floating point. He has also made a careful study of how to make branch cuts in the complex plane so as to allow evaluation of the elementary functions without any anomalies....

Topics: DTIC Archive, Kahan, W, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

We have discovered a new implementation of the qd algorithm that has a far wider domain of stability than Rutishauser's version. Our algorithm was developed from an examination of the LR-Cholesky transformation and can be adapted to parallel computation in stark contrast to traditional qd. Our algorithm also yields useful a posteriori upper and lower bounds on the smallest singular value of a bidiagonal matrix. The zero-shift bidiagonal QR of Demmel and Kahan computes the smallest singular...

Topics: DTIC Archive, Fernando, K. V., CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

New methods for scaling square, nonnegative matrices to doubly stochastic form are described. A generalized version of the convergence theorem in SINKHORN and KNOPP 1967 is proved and applied to show convergence for these new methods. Tests indicate that one of the new methods has significantly better average and worst-case behavior than the Sinkhorn/Knopp methods; for one of the 3X3 examples in MARSHALL and OLKIN 1968, SK requires 130 times as many operations as the new algorithm to achieve...

Topics: DTIC Archive, Parlett, B N, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

A baclund transformation and linearization for an instance of the henon heiles system is examined. This provides a special form of solution depending on the three parameters. In addition, a direct formulation in terms of the schwarzian derivative is defined for the henon heiles system and second Painleve transcendent. This provides (1) a classification of the Henon Heiles system as equations of Novikov type and; (2) a simple method for deriving the Backlund transformations and special solutions...

Topics: DTIC Archive, Weiss,John, CALIFORNIA UNIV SAN DIEGO LA JOLLA INST FOR PURE AND APPLIED PHYSICAL...

This research has led to new developments for solving nonlinear optimization problems involving functions that are not everywhere differentiable and/or are implicity defined. For the single variable case a method has been given which combined polyhedral and quadratic approximation, and automatic scale-free penalty technique and a safeguard that insures convergence to a stationary point, but does not detract from rapid convergence. Under relatively weak convergence rate assumptions the algorithm...

Topics: DTIC Archive, Mifflin,R, WASHINGTON STATE UNIV PULLMAN DEPT OF PURE AND APPLIED MATHEMATICS,...

The implicit Cholesky algorithm has been developed by several authors during the last 10 years but under different names. We identify the algorithm with a special version of Rutishauser's LR algorithm. Intermediate quantities in the transformation furnish several attractive approximations to the smallest singular value. The paper extols the advantages of using shifts with the algorithm. The nonorthogonal transformations improve accuracy.

Topics: DTIC Archive, Fernando, K. V., CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

Contents: An Outline of His Career; Background; Roundoff Error Analysis; The Linear Equation Problem; The Eigenvalue Problem; The Zeros of Polynomials. (kr)

Topics: DTIC Archive, Parlett, Beresford N, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED...

A procedure for deriving the Lanczos Coordinates is explained and their use in structural dynamics analysis as an alternative to modal coordinates is discussed. The coordinates are obtained by an inverse iteration procedure in which orthogonality is imposed between the vectors resulting from successive iteration cycles. Using these Lanczos coordinates the equations of motion are transformed to tridiagonal form, which provides for very efficient time-stepping solution. The effectiveness of the...

Topics: DTIC Archive, Nour-Omid,B, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

The goal is to compute eigenvectors of a symmetric tridiagonal matrix T that are orthogonal to working accuracy. Consider a cluster of m very close eigenvalues that are reasonably well separated from the remaining spectrum. We show here that there are m principal submatrices of T such that only the nearest neighbors overlap and each submatrix has a simple, isolated eigenvalue in the convex hull of the cluster with eigenvector having small entries in the first and last positions. This...

Topics: DTIC Archive, Parlett, Beresford, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

Consider the task of finding all the eigenvalues of a dense matrix. We show how Hadamard's procedure (1891) can be organized into Aitken's H-table (1925) and how the H-table may be transformed into Rutishauser's qd-array (1953) with the help of the Lanczos algorithm. We show how the qd algorithm can be interpreted as defining the LR algorithm (1958). Finally we show how the original qd algorithm may be transformed into the shifted differential qd algorithm dqds developed by Fernando and Parlett...

Topics: DTIC Archive, Parlett, Beresford N., CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED...

This document describes a program to compute the exponential of a given n by n matrix B multiplied by a scalar tau that is to be thought of as representing time. The authors' primary goal has been to achieve as much accuracy as working precision permits without resorting to stimulated higher precision. The final product is more complicated than they anticipated at the outset. How these complications came to be expected is the theme of this story. The cases considered may be of interest to those...

Topics: DTIC Archive, Parlett,B N, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

The research program includes both ongoing experiments and theory on transport in pure electron plasmas; and the design, construction and operation of a new pure ion plasma apparatus. Recent experiments on the electron apparatus have elucidated the transport and turbulence associated with diocotron instabilities and vortex structures, and have measured the vortex pairing instability in detail. Recent theory work has analyzed the newly observed diocotron instability, analyzed negative...

Topics: DTIC Archive, Malmberg, J H, CALIFORNIA UNIV SAN DIEGO LA JOLLA INST FOR PURE AND APPLIED PHYSICAL...

This paper concerns Hamiltonian and non-Hamiltonian perturbations of integrable two degree of freedom Hamiltonian systems which contain homoclinic and periodic orbits. Our main example concerns perturbations of the uncoupled system consisting of the simple pendulum and the harmonic oscillator. We show that small coupling perturbations with, possibly, the addition of positive and negative dampling breaks the integrability by introducing horseshoes into the dynamics. (Author)

Topics: DTIC Archive, Holmes,Philip J, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

Using x-rays of 60-200 keV photon energy (lambda ranges 0.06 to 0.2 A) as an ionizing radiation source in a transmission-line-driven, low-inductance discharge chamber, we have succeeded in generating spatially-homogeneous pulsed avalanche discharges of several liter volume at greater than 1 atm pressure for up to 100 nsec duration. In concurrent laser generation experiments with relatively lossy windows, we have observed high optical quality pulsed uv laser output of up to 2 J/liter from such...

Topics: DTIC Archive, Lin,Shao-Chi, CALIFORNIA UNIV SAN DIEGO LA JOLLA INST FOR PURE AND APPLIED PHYSICAL...

This report describes the work carried out during the first three years of research devoted to aerosol studies. Some preliminary measurements have been made primarily to ensure the accurate and reliable operation of the various devices installed rather than with any closely defined specific scientific goals in mind at this time. However, two specific aerosol projects have been conducted during this period. The former project is a laboratory investigation of the effects of mixing on the...

Topics: DTIC Archive, Latham,John, Gay,M J, UNIVERSITY OF MANCHESTER INST OF SCIENCE AND TECHNOLOGY...

The Ising model was proposed to explain properties of ferromagnets but since then it has found application to topics in Chemistry and Biology as well as in Physics. For any reader unfamiliar with the model an excellent introduction targeted at a general audience is Cip87. The remainder of this section assumes some knowledge of the so called transfer matrix. This paper presents a numerical method for computing properties of the 2D Ising model for given parameter values such as magnetic field...

Topics: DTIC Archive, Parlett, Beresford, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

The researchers undertook an examination of many of the mathematical issues that are well understood in the case of the medical application of these tomographic ideas (i.e. x-ray scanners) but have not yet been explored in the arena of radar imaging. Among the issues concentrated on were: (1) an understanding of the way in which data might be collected in radar, (2) the proper interpretation of these data as projections of a two dimensional distribution in range-Doppler space, (3) a careful...

Topics: DTIC Archive, Grunbaum, F A, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

Data from UCSD plasma instruments on the ATS 5 and 6 satellites has been studied to specify the geosynchronous plasma environment as it affects electrostatic charging of spacecraft. The emphasis of the initial study has been primarily to service the needs of the design engineer; while simultaneously establishing the context in which a more general model could be developed. The report includes an environmental specification plus a review of geosynchronous plasma and wave phenomena. (Author)

Topics: DTIC Archive, DeForest,Sherman E, CALIFORNIA UNIV SAN DIEGO LA JOLLA INST FOR PURE AND APPLIED...

A method for the analysis of perturbations of integrable planar systems of differential equations is developed. Concentrating on the case in which the unperturbed system is Hamiltonian and the perturbation introduces dissipation and time-periodic forcing, the global solution curves of the unperturbed system are used in regular perturbation calculations to locate subharmonic orbits and homoclinic orbits and to characterize the bifurcations in which they are created as external parameters are...

Topics: DTIC Archive, Greenspan, Bernie D., CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED...

During the past five years four distinct advances in the science of superconductivity have been made: (1) many new superconductors were discovered, including lithium-titanate (Tc = 13.7K) and numerous Chevrel phases (Tc = 15.2K lead-molybenum-sulfide). The latter are remarkable not only for their extra-ordinarily high critical fields, which are close to 700 kg in some cases, but also for the fact that really high critical temperatures have for the first time been discovered in non-cubic...

Topics: DTIC Archive, Matthias,Bernd T, CALIFORNIA UNIV SAN DIEGO LA JOLLA INST FOR PURE AND APPLIED...

The first part of this report details a review of the dispersion of pollutants by rainfall, with particular reference to inertial and diffusive removal by precipitation, inertial, condensational and diffusive removal by cloud drops, and the influence of electrical forces on scavenging. The second half of the report describes a preliminary study of the influence of meteorological parameters on the size distribution of natural aerosol particles, with particular reference to two data sets obtained...

Topics: DTIC Archive, Gay,M J, UNIVERSITY OF MANCHESTER INST OF SCIENCE AND TECHNOLOGY (ENGLAND) DEPT OF...

The eigenvalue problem for large, sparse matrices is not yet understood well enough, in all its computational ramifications, to permit the rapid deployment of impeccable software to the masses in the style set by EISPACK. Indeed it is doubtful that the public is impatient for the arrival of this facility. Those with an urgent need for such software prize efficiency above generality. They have developed their own programs independently of the numerical analysts and will continue to do so unless...

Topics: DTIC Archive, Parlett,B N, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

In the laboratory, the interactions of ice crystals with rime coated targets provides a simulation of the charging of graupel pellets in thunderstorms. The experimental techniques used in previous studies have come under criticism and this study examines the importance of the precise conditions used in the laboratory measurements.

Topics: DTIC Archive, Saunders, Clive, UNIVERSITY OF MANCHESTER INST OF SCIENCE AND TECHNOLOGY (UNITED...

We start with an unperturbed system containing a homoclinic orbit and at least two families of periodic orbits associated with action angle coordinates. We use KAM theory to show that some of the resulting tori persist under small perturbations and use a vector of Melkinov integrals to show that, under suitable hypotheses, their stable and unstable manifolds intersect transversally. This transverse intersection is ultimately responsible for Arnold diffusion on each energy surface. The method is...

Topics: DTIC Archive, Holmes,Philip J, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

The traditional recurrence for the computation of exponential divided differences, along with a new method based on the properties of the exponential function, are studied in detail in this paper. Our results show that it is possible to combine these two methods to compute exponential divided differences accurately. A hybrid algorithm is presented for which our error bound grows quite slowly with the order of the divided difference. (Author)

Topics: DTIC Archive, McCurdy,A C, CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS,...

The report covers work carried out by students at the University of Strathclyde evaluating the application of the dielectric technique to the characterisation of ageing in adhesive bonded structures. The work covers studies of aluminium-epoxy-aluminium and carbon fibre-epoxy-carbon fibre. The ageing in these structures was induced by exposing samples to high humidity and elevated temperatures and revealed the possible correlations between the changes in dielectric property and changes in...

Topics: DTIC Archive, Pethrick, R A, STRATHCLYDE UNIV GLASGOW (UNITED KINGDOM) DEPT OF PURE AND APPLIED...

As specified in the original proposal, there exits mounting evidence that the growth of strong electric fields - culminating in lightning - in the great majority of thunderstorms is intimately linked with - and probably contingent upon - the concomitant development of the ice-phase. Thus, significant progress in the elucidation of electrification mechanisms requires an improved understanding of the complex set of processes involved in cloud glaciation. Accordingly, primary emphasis has been...

Topics: DTIC Archive, Latham, John, UNIVERSITY OF MANCHESTER INST OF SCIENCE AND TECHNOLOGY (UNITED...